1. Field of the Invention
The invention relates generally to the field of seismic data processing. More specifically, the invention relates to methods for migrating seismic data to correct arrival times and apparent depths of reflective events for changes in the contour of subsurface reflective horizons and for changes in velocity of the formations through which seismic energy propagates.
2. Background Art
Seismic surveying is used to determine structures of, to determine compositions of, and to determine fluid content of subsurface earth formations, among other uses. A particular application for seismic surveying is to infer the presence of useful materials, such as petroleum, in the subsurface earth formations. Generally, seismic surveying includes deploying an array of seismic sensors at or near the earth's surface at selected geographic positions, and deploying one or more seismic energy sources at selected locations, also at or near the earth's surface. The one or more seismic energy sources are actuated and seismic energy emanates from the source(s), traveling generally downwardly through the earth's subsurface until it reaches one or more acoustic impedance boundaries in the earth. Seismic energy is reflected from the one or more impedance boundaries, where it then travels upwardly until being detected by one or more of the seismic sensors. Structure and composition of the earth's subsurface is inferred from the travel time of the reflected seismic energy, from the geographic position of the source to each of the sensors and from the amplitude and phase of the various frequency components of the reflected seismic energy with respect to the energy emanating from the seismic source.
Structures of the earth's subsurface are inferred from the travel time of the seismic energy from the source to the acoustic impedance boundaries and back to the seismic sensors at the surface. In order to infer depth of and the structures of subsurface earth formations from reflection seismic travel times measured at the earth's surface, it is necessary to determine the acoustic velocity of the various formations through which the seismic energy passes. Velocities of the earth formations can vary both with respect to depth in the earth (vertically), and with respect to geographic position (laterally). Seismic data, however, are recorded only with respect to time. Methods known in the art for estimating velocities of the earth formations both vertically and laterally rely on inferences about the travel path geometry of the seismic energy as it travels from the seismic source to the various seismic receivers deployed at or near the earth's surface.
Migration is a process performed on seismic data in which depth estimates to one or more reflective horizons (acoustic impedance boundaries) in the earth are made from the “two-way” travel time of seismic energy from the seismic energy source to the reflective horizons and back to the seismic receivers. The depth estimates of the reflective horizons are computed and are displayed with respect to geographic position. Depth estimates based on two-way travel time must be corrected for energy travel path differences between the various seismic energy source and receiver geographic positions that are used during data acquisition. In order to correct the depth estimates for the various source and receiver positions, it is necessary to accurately estimate the velocity of seismic energy in the earth from the earth's surface (or the ocean bottom in marine seismic data) to each subsurface reflective horizon. Methods are known in the art for estimating velocity from two-way travel time from the seismic source to the reflective horizons and back to the seismic receivers. One such method uses two-way travel times for source and receiver arrangements which have a “common mid point” along the seismic energy travel path. Acoustic velocities of the earth formations from the earth's surface to a particular subsurface reflector can be estimated using the familiar Dix equation, for example. Other methods for estimating velocity are known in the art.
According to wave propagation theory well known to those skilled in the art, a spherical seismic energy wave propagating from a “point” source (a source modeled for calculation purposes as having essentially zero volume or spatial extent) can be decomposed into a series of plane waves. See, for example, Stoffa, P. L., Buhl, P., Diebold, J. B., and Wenzel, F., Direct mapping of seismic data to the domain of intercept time and ray parameter—A plane-wave decomposition: Geophysics, 46, 410–421 (1981). The Stoffa et al. article describes a method for decomposing seismic reflection data into plane waves by slant stacking, i.e., transforming seismic data into the plane wave (τ-p) domain (τ=intercept time and p=ray parameter), and further documents some advantages of processing seismic data in the plane wave (τ-p) domain, including, for example, linear noise attenuation or normal move-out in a horizontally stratified medium without approximation. Using stacking velocity analysis performed in the offset-time (x-t) domain, by contrast, provides RMS (root mean square) velocities. The RMS velocities can then be converted into interval velocities when required. Advantageously, velocity analysis in the plane-wave domain results in the estimation of interval velocities directly. Having accurate estimates of interval velocities is important for performing migration.
Some of the research in prestack migration velocity analysis began in the early 1990's. See, for example, Al-Yahya, K., Velocity analysis by iterative profile migration, Geophysics, vol. 54, pp. 718–729 (1989). Various analytic functions have been derived to express the relationship between the true velocity (or the ratio of the migration velocity and the true velocity) and the offset in a common image gather (CIG) in the depth-offset domain after migration. The foregoing analytic functions make use of the assumptions of a small dip (rate of change of depth with respect to lateral displacement), small offset, and/or constant velocity in the various layers of the earth's subsurface. Residual moveout analysis has also been used to extend the application of such analytic functions to media having lateral velocity variation. See, for example, Meng, Z, Bleistein, N, and Wyatt, K. D, 3-D Analytical migration velocity analysis I: Two-step velocity estimation by reflector-normal update, 69th Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts (1999).
Most of the migration methods known in the art are implemented in the depth-offset domain (z-x), and a top-down “layer stripping” migration method is then used to derive the interval velocities. It is known in the art to use the depth-offset domain because this is the domain in which most prestack depth migration is performed, and the domain in which migrated CIG's are available for analysis. However, it is also known in the art to perform prestack depth migration in the plane-wave (τ-p) domain. See, for example, Akbar, F. E., Sen, M. K., and Stoffa, P. L, Prestack plane-wave Kirchhoff migration in laterally varying media, Geophysics, 61, 1068–1079 (1996). See also, Tanis, M. C., Prestack Split-step Fourier Depth Migration Algorithms and Parallel Implementation on Cray T3E, Ph.D. Dissertation, The University of Texas at Austin (1998). After migration in the plane wave domain, seismic data are displayed or presented in the depth-plane wave (z-p) domain. Prestack depth migration using slant stack (τ-p) data and a substantially correct interval velocity-depth model generate events in a common image gather (CIG) in the depth-plane wave (z-p) domain which are substantially horizontally aligned, because a CIG represents an image of the same subsurface position obtained along different seismic travel path angles. See, for example, Whitmore, N. D. and Garing, J. D., Interval velocity estimation using iterative prestack depth migration in the constant angle domain, The Leading Edge, vol. 12, no. 7, pp. 757–762 (1993).
Use of an erroneous velocity-depth model in migration, however, can cause misalignment of reflective events in a CIG, meaning that the reflective events displayed on the CIG exhibit a residual “moveout.” By analyzing the residual moveout (a change in apparent depth with respect to ray parameter) in the CIG, it is possible to derive depth and velocity corrections, thus obtaining an updated velocity-depth model. For example, if the velocity used in the migration process is lower than the true velocity, the event appears to curve upwardly in the depth-plane wave (z-p) domain after prestack depth migration. If the velocity used in the migration process is higher than the true velocity, then the events in the CIG appear to curve downwardly.
For some time, a method known as the “vertical velocity update method” has been used to generate a velocity-depth model for prestack depth migration. A typical data processing procedure used in such methods is known as the “Deregowski loop.” See Deregowski, S. M., Common-offset migrations and velocity analysis, First Break, vol. 8, no. 6, pp. 224–234 (1990). Residual velocity analysis can be applied at all depths based on the constant velocity assumption. See, Al-Yahya, K. (1989), Velocity analysis by iterative profile migration, Geophysics, vol. 54, pp. 718–729. Then the constant velocities are converted to interval velocities for a subsequent iteration. If it is desired to obtain the interval velocities from migrated seismic data directly, it is necessary to perform both prestack depth migration and the velocity analysis in a top-down “layer-stripping” procedure.
More recently, a method has been developed to update interval velocities using residual analysis in the depth-plane wave domain. See, Jiao, J., Stoffa, P., Sen, M., and Seifoullaev, R., Residual migration velocity analysis in the plane-wave domain, Geophysics, vol. 67, pp. 1258–1269 (2002). See also, Jiao, J., Residual Migration Velocity Analysis in The Plane Wave Domain: Theory and Applications, Ph.D. Dissertation, The University of Texas at Austin (2001). The method disclosed in the foregoing reference eliminates the need to perform “layer-stripping” prestack depth migration in order to obtain interval velocities. However, the method disclosed in the Jiao et al. article requires that prestack migration be performed in the depth-plane wave domain (z-p), which limits the application of that method. It is desirable to have a method for performing prestack migration in the depth-offset (z-p) domain which includes updating of interval velocities.